Abstract
The methods of Dyson, Lieb, and Simon are extended to prove the existence of Néel order in the ground state of the 3D spin-1/2 Heisenberg antiferromagnet on the cubic lattice. We also consider the spin-1/2 antiferromagnet on the cubic lattice with the coupling in one of the three lattice directions taken to be r times its value in the other two lattice directions. We prove the existence of Néel order for 0.16≤r≤1. For the 2D spin-1/2 model we give a series of inequalities which involve the two-point function only at short distances and each of which would by itself imply Néel order.
Original language | English (US) |
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Pages (from-to) | 1019-1030 |
Number of pages | 12 |
Journal | Journal of Statistical Physics |
Volume | 53 |
Issue number | 5-6 |
DOIs | |
State | Published - Dec 1988 |
Keywords
- Gaussian domination
- Néel order
- infrared bounds
- spin-1/2 antiferromagnets
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics